---
title: "Tile drain spacing: rainfall 1400 mm"
subject: "Irrigation and Drainage Engineering"
chapter: 9
key: "semester_6/irrigation_and_drainage_engineering:tile-drain-rainfall-1400-1pct"
source: https://www.bctengineer.com/q/semester_6/irrigation_and_drainage_engineering/tile-drain-rainfall-1400-1pct
site: BCT Engineering
---

# Tile drain spacing: rainfall 1400 mm

Irrigation and Drainage Engineering · Chapter 9: Water Logging and Drainage

- Asked in: 2068 Baisakh (old course), 8 marks
- Video: [Unit:7 | Water logging & Drainage | Numerical | Irrigation Engineering | BE Civil | TU,PU,KU,PoU |](https://www.youtube.com/watch?v=csVF08cgXmc) — Prashant YT
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/irrigation_and_drainage_engineering/tile-drain-rainfall-1400-1pct
- Whole chapter: https://www.bctengineer.com/md/semester_6/irrigation_and_drainage_engineering/chapter-9

## Question

Find the spacing of the tile drains for an area having average annual rainfall of 1400 mm, if 1% is to be drained in 24 hours. From ground level, depth of impervious stratum = 9 m; depth of drains = 2 m and depth of highest position of the water table = 1 m. Coefficient of permeability may be taken as 0.001 cm/sec.

## Short answer

Donnan's formula S = sqrt[4K(b²-a²)/q]: K=1×10⁻⁵ m/s, q = 1% of 1400 mm in 24 h = 1.62×10⁻⁷ m/s, a=7 m, b=8 m. Spacing S ≈ 60.9 m (say 61 m).

## Answer

Tile drain spacing is found from Donnan's (Dupuit–Forchheimer) formula for steady flow towards parallel drains over an impervious layer:

$$
S=\sqrt{\frac{4K\,(b^2-a^2)}{q}}
$$

where $S$ = spacing, $K$ = permeability, $q$ = drainage rate (discharge per unit area), $b$ = height of the water table above the impervious layer at the mid-point, $a$ = height of the drain above the impervious layer.

#### Data
- Depth of impervious layer = 9 m, depth of drain = 2 m, depth of highest water table = 1 m (all below ground)
- $K$ = 0.001 cm/s = $1\times10^{-5}$ m/s
- Rainfall 1400 mm; 1 % to be drained in 24 hours

#### Step 1: Drainage rate
$$
q = \frac{1}{100}\times\frac{1400}{1000}\ \text{m} \Big/ (24\times3600\ \text{s}) = 1.62\times10^{-7}\ \text{m/s}
$$

#### Step 2: Heights above the impervious layer
$$
\begin{aligned} a &= 9-2 = 7\ \text{m} \\ b &= 9-1 = 8\ \text{m} \end{aligned}
$$

#### Step 3: Spacing
$$
\begin{aligned} S^2 &= \frac{4\times1\times10^{-5}\times(8^2-7^2)}{1.62\times10^{-7}} \\ &= \frac{4\times1\times10^{-5}\times15.00}{1.62\times10^{-7}} = 3703\ \text{m}^2 \\ S &= 60.9\ \text{m} \end{aligned}
$$

**Answer: spacing of the tile drains ≈ 60.9 m (say 61 m).**

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. What is q when 1% of 1400 mm is drained in 24 hours?
   A. 1.62 x 10^-7 m/s (14 mm/day)
   B. 1.62 x 10^-5 m/s
   C. 1.4 x 10^-7 m/s
   D. 14 x 10^-7 m/s
   Answer: A. q = 0.01 x 1.4 m / 86400 s = 1.62e-7 m/s. (Key point: Drainage rate)

2. What are a and b (impervious 9 m, drains 2 m, water table 1 m below ground)?
   A. a = 8 m, b = 7 m
   B. a = 7 m, b = 8 m
   C. a = 2 m, b = 1 m
   D. a = 9 m, b = 8 m
   Answer: B. Heights above the impervious layer: 9 - 2 = 7 and 9 - 1 = 8. (Key point: Heights)

3. Compared with 1.5% of 1600 mm (46.5 m), why is this spacing larger?
   A. The rainfall is larger
   B. K is smaller
   C. The required drainage rate q is smaller and S varies as 1/sqrt(q)
   D. The drain is deeper
   Answer: C. Same K, a and b but lower q, so spacing increases to 60.9 m. (Key point: Effect of q)

4. What is the calculated spacing?
   A. About 37 m
   B. About 3703 m
   C. About 15 m
   D. About 60.9 m
   Answer: D. S^2 = 4e-5 x 15/1.62e-7 = 3703 m^2, S = 60.9 m. (Key point: Spacing)

## Close variants set in other exams

- [Tile drain spacing: rainfall 1600 mm](https://www.bctengineer.com/question.md?key=semester_6%2Firrigation_and_drainage_engineering%3Atile-drain-rainfall-1600-impervious9) — Irrigation and Drainage Engineering, chapter 9, asked 3×

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